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Least totients in arithmetic progressions.
- Source :
-
Proceedings of the American Mathematical Society . Apr2009, Vol. 137 Issue 9, p2913-2919. 7p. - Publication Year :
- 2009
-
Abstract
- Let $N(a,m)$ be the least integer $n$ (if it exists) such that $varphi (n)equiv apmod m$. Friedlander and Shparlinski proved that for any $varepsilon >0$ there exists $A=A(varepsilon )>0$ such that for any positive integer $m$ which has no prime divisors $p<(log m)^A$ and any integer $a$ with $gcd (a,m)=1,$ we have the bound $N(a,m)ll m^{3+varepsilon }.$ In the present paper we improve this bound to $N(a,m)ll m^{2+varepsilon }.$ [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICAL proofs
*NUMERICAL analysis
*MATHEMATICS
*ARITHMETIC series
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 137
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 46876862
- Full Text :
- https://doi.org/10.1090/S0002-9939-09-09864-5